Solve {l}{3cx+2y=2y}{2cy+s=7x}

$$\left\{ \begin{array} { l } { 3 c x + 2 y = 2 y } \\ { 2 c y + s = 7 x } \end{array} \right.$$

Solve for x, y (complex solution)

$$\left\{\begin{matrix}x=0\text{, }y=-\frac{s}{2c}\text{, }&c\neq 0\\x=0\text{, }y\in \mathrm{C}\text{, }&s=0\text{ and }c=0\\x=\frac{s}{7}\text{, }y=0\text{, }&s=0\text{ or }c=0\\x=\frac{s}{7}\text{, }y\in \mathrm{C}\text{, }&c=0\end{matrix}\right.$$

Steps Using Substitution

Consider the first equation. Subtract 2y from both sides.

$$3cx+2y-2y=0$$

Combine 2y and -2y to get 0.

$$3cx=0$$

Consider the second equation. Subtract 7x from both sides.

$$2cy+s-7x=0$$

Subtract s from both sides. Anything subtracted from zero gives its negation.

$$2cy-7x=-s$$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$3cx=0,-7x+2cy=-s$$

Pick one of the two equations which is more simple to solve for x by isolating x on the left hand side of the equal sign.

$$3cx=0$$

Divide both sides by 3c.

$$x=0$$

Substitute 0 for x in the other equation, -7x+2cy=-s.

$$2cy=-s$$

Divide both sides by 2c.

$$y=-\frac{s}{2c}$$

The system is now solved.

$$x=0,y=-\frac{s}{2c}$$

Solve for x, y

$$\left\{\begin{matrix}x=0\text{, }y=-\frac{s}{2c}\text{, }&c\neq 0\\x=0\text{, }y\in \mathrm{R}\text{, }&s=0\text{ and }c=0\\x=\frac{s}{7}\text{, }y=0\text{, }&s=0\text{ or }c=0\\x=\frac{s}{7}\text{, }y\in \mathrm{R}\text{, }&c=0\end{matrix}\right.$$

Steps Using Substitution

Consider the first equation. Subtract 2y from both sides.

$$3cx+2y-2y=0$$

Combine 2y and -2y to get 0.

$$3cx=0$$

Consider the second equation. Subtract 7x from both sides.

$$2cy+s-7x=0$$

Subtract s from both sides. Anything subtracted from zero gives its negation.

$$2cy-7x=-s$$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$3cx=0,-7x+2cy=-s$$

Pick one of the two equations which is more simple to solve for x by isolating x on the left hand side of the equal sign.

$$3cx=0$$

Divide both sides by 3c.

$$x=0$$

Substitute 0 for x in the other equation, -7x+2cy=-s.

$$2cy=-s$$

Divide both sides by 2c.

$$y=-\frac{s}{2c}$$

The system is now solved.

$$x=0,y=-\frac{s}{2c}$$